Finite Sample and Large Deviations Analysis of Stochastic Gradient Algorithm with Correlated Noise

TL;DR

This paper provides a detailed analysis of the finite sample performance and large deviations behavior of stochastic gradient algorithms with correlated noise, using Lyapunov functions and large deviations theory.

Contribution

It introduces a systematic approach for analyzing stochastic gradient algorithms with correlated noise, focusing on finite sample regret and escape times.

Findings

Finite sample regret bounds derived for correlated noise scenarios.

Analysis of escape times using large deviations theory.

Methodology employing perturbed Lyapunov functions for convergence analysis.

Abstract

We analyze the finite sample regret of a decreasing step size stochastic gradient algorithm. We assume correlated noise and use a perturbed Lyapunov function as a systematic approach for the analysis. Finally we analyze the escape time of the iterates using large deviations theory.